Revisiting the phenomenon of bouncing of inertial particles crossing density stratified interfaces

TL;DR

This study experimentally explores how inertial particles bounce or settle through density-stratified interfaces, revealing that the ratio of particle Froude numbers, influenced by inertia and viscosity, governs bouncing behavior.

Contribution

It introduces a new critical ratio of particle Froude numbers that predicts bouncing, extending previous models to include viscosity effects and providing insights into particle retention in stratified fluids.

Findings

Bouncing occurs when $Fr_2/Fr_1 \, \le \, 0.142$

Existing models based on density ratios are insufficient

Viscosity contrasts significantly influence particle dynamics

Abstract

We experimentally investigate the dynamics of inertial spheres settling through density-stratified interfaces, focusing on the conditions that lead to pronounced deceleration and ``bouncing''. Using synchronized particle tracking and flow visualization in both water-salt and water-glycerol stratifications, we extend the parameter space of previous studies to include significant viscosity contrasts. We show that existing models based solely on density ratios fail to capture the observed retention times and bouncing behavior. Instead, we identify the ratio of particle Froude numbers across the interface, $Fr_2/Fr_1 \le 0.142$, as the critical condition distinguishing bouncing from non-bouncing cases. Using a drag-law of the form $C_d = \alpha Re^{-\beta}$, this ratio can be expressed in terms of density and viscosity contrasts. The results reveal how inertia, viscosity, and stratification jointly control particle retention, with implications for sedimentation, separation, and biogeophysical transport processes.